1. Field of the Invention
The present invention relates to a measuring apparatus including a multi-wavelength interferometer.
2. Description of the Related Art
As an apparatus for measuring a shape of a surface to be inspected of an object or goods with a high degree of accuracy, generally, a heterodyne interferometry method is known. In a single wavelength interferometer (see Patent Document 1 (Japanese Patent Laid-Open No. 10-185529)), when a surface to be inspected is rough, a speckle pattern caused by the roughness of the surface has a random phase with a standard deviation greater than 2π, so that uncertainty of measurement increases and an accurate measurement is difficult to be performed.
As a method to solve the above problem, it is described that, in an apparatus that projects laser light to a surface of an object and captures an image of reflected light, incoherent averaging of the random phase of the speckle pattern is performed by changing an aperture position of an imaging lens (see Patent Document 2 (Japanese Patent Laid-Open No. 5-71918)).
As another solving means, a multi-wavelength interferometer is known which synthesizes phases of wavelengths from an interference measurement result of a plurality of different wavelengths (see Non-Patent Document 1 (A. F. Fercher et al., “Rough-surface interferometry with a two-wavelength heterodyne speckle interferometer”, Applied Optics, 1985, vol. 24, issue 14, pp 2181-2188)). According to Non-Patent Document 1, if there is a correlation between speckles of two wavelengths, it is possible to obtain information related to a macroscopic surface profile and a microscopic surface roughness on the basis of a phase difference between the two wavelengths.
It is known that a correlation of speckle pattern between two wavelengths depends on a synthesized wavelength of the two wavelengths (see Non-Patent Document 2 (U. Vry, F. Fercher, “High-order statistical properties of speckle fields and their application to rough-surface interferometry”, J. Opt. Soc. Am. A, 1986, vol. 3, issue 7, pp 988-1000)). The higher the degree of coincidence of the two speckle patterns, the higher the degree of correlation. According to Non-Patent Document 2, the smaller the synthesized wavelength Λ, the smaller the correlation of speckle pattern between the two wavelength, and conversely, the greater the synthesized wavelength Λ, the greater the correlation of speckle pattern between the two wavelength. Here, the synthesized wavelength Λ is a value represented by Λ=λ1×λ2/(λ1−λ2) when the two wavelengths are λ1 and λ2 (λ1>λ2). In this way, the multi-wavelength interferometer can accurately measure a rough surface to be inspected, which is difficult to measure by the single wavelength interferometer.
According to Non-Patent Document 2, the correlation of speckle pattern between two wavelengths depends on a size of synthesized wavelength as well as roughness of the surface to be inspected and inclination of the surface to be inspected (see Formula 1).
                    μ        =                              exp            ⁡                          (                                                                    4                    ⁢                    π                    ⁢                                                                                  ⁢                    ⅈ                                    Λ                                ⁢                                  h                  0                                            )                                ×                      exp            ⁡                          [                                                -                                                            4                      ⁢                                              π                        2                                                                                    Λ                      2                                                                      ⁢                                  (                                                            2                      ⁢                                              σ                        h                        2                                                              +                                                                  s                        2                                            ⁢                                              a                        2                                                                              )                                            ]                                                          Formula        ⁢                                  ⁢        1            
Here, μ represents a complex correlation function between two wavelengths, h0 represents a height of the surface to be inspected, and Λ represents a synthesized wavelength of the two wavelengths. Further, σh represents a roughness of the surface to be inspected, s represents an inclination of the surface to be inspected, and a represents a diameter when the surface to be inspected is irradiated by a Gaussian beam. According to Formula 1, when the roughness of the surface to be inspected increases, the correlation of speckle between the two wavelengths decreases. When the inclination of the surface to be inspected increases, the correlation of speckle between the two wavelengths decreases. In particular, influence of the inclination of the surface to be inspected to the correlation of speckle between the two wavelengths is large. FIG. 1 shows an example of a relationship between an inclination angle of the surface to be inspected and a length measurement error. FIG. 1 is a result of a simulation of a length measurement error, in which the surface to be inspected having a roughness of Ra 0.4 μm is illuminated by a spot size of 65 μm and measured by a two-wavelength interferometer which has a synthesized wavelength of 300 μm and receives light of a range of NA 0.02. Here, the length measurement error is a value of 2σ of length measurement errors of 100 samples of the surface to be inspected. According to FIG. 1, when the inclination of the surface to be inspected is 0°, the length measurement error is as small as 0.6 μm. However, when the inclination of the surface to be inspected is 10°, the length measurement error significantly deteriorates to 8.1 μm. Normally, a speckle pattern in a pupil conjugate plane (a plane related to Fourier transform) with respect to the surface to be inspected when the surface to be inspected is inclined is formed as a pattern in which a speckle pattern when the surface to be inspected is not inclined is shifted (moved in a horizontal direction) in a pupil plane. When the surface to be inspected is inclined, there is a difference between shift amounts of the speckle patterns in a pupil plane of different wavelengths λ1 and λ2 formed in a pupil conjugate plane of the surface to be inspected, so that the correlation of speckle pattern between the two wavelengths decreases and the degree of accuracy of the length measurement deteriorates. Further, when the inclination angle of the surface to be inspected increases, the difference of the shift amount between the speckle patterns in the pupil plane of the two wavelengths increases, the correlation of speckle pattern between the two wavelengths further decreases and the degree of accuracy of the length measurement significantly deteriorates. As described above, even when a multi-wavelength interferometer is used to measure a rough surface, if the surface to be inspected is inclined, it is difficult to perform an accurate measurement due to decrease of the correlation between the wavelengths.